A340740 a(n) is the sum of all the remainders when n is divided by positive integers less than n/2 and coprime to n.

0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 7, 2, 7, 6, 5, 4, 15, 7, 19, 10, 9, 8, 32, 9, 20, 20, 28, 13, 46, 14, 47, 31, 27, 31, 48, 17, 62, 39, 58, 26, 87, 26, 94, 53, 52, 41, 127, 48, 100, 65, 79, 61, 154, 52, 105, 62, 90, 80, 200, 45, 180, 113, 138, 103, 162, 77, 229, 116, 149, 73, 274, 87, 257, 166, 178

Offset

1,7

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..floor((n-1)/2)} (n mod k) * floor(1/gcd(n,k)). - Wesley Ivan Hurt, Jan 18 2021

Example

For n = 11, a(11) = (11 mod 1)+(11 mod 2)+(11 mod 3)+(11 mod 4)+(11 mod 5) = 7.

Maple

f:= proc(n) local k;
  add(`if`(igcd(k, n)=1, n mod k, 0), k=1..floor(n/2))
end proc:
map(f, [$1..100]);

Mathematica

Table[Sum[Mod[n, i]*Floor[1/GCD[i, n]], {i, Floor[(n - 1)/2]}], {n,
100}] (* Wesley Ivan Hurt, Jan 18 2021 *)

Prog

(PARI) a(n) = sum(k=1, n\2, if (gcd(k, n)==1, n%k)); \\ Michel Marcus, Jan 18 2021
(Python)
from math import gcd
def A340740(n): return sum(n % k for k in range(1, n//2+1) if gcd(k, n) == 1) # Chai Wah Wu, Mar 18 2021

Crossrefs

Cf. A067439.

Sequence in context: A352736 A086612 A128207 * A306707 A180958 A295854

Adjacent sequences: A340737 A340738 A340739 * A340741 A340742 A340743

Keyword

nonn,look

Author

J. M. Bergot and Robert Israel, Jan 18 2021

Status

approved